BSTJ 10: 1. January 1931: The Detection of Two Modulated Waves Which Differ Slightly in Carrier Frequency. (Aiken, Charles B.)

9.6 MB·English

The Bell System Technical Journal

Famarg, 1984

‘The Detection of Two Modulated Waves Which Differ
Slightly in Carrier Frequency *

Teese eh inal een ot che Sipser ant

VV HEXEVER se of mo stato opuatig on te sane sae

‘cogil essisomec: wandsis from Ite proper fecqueacy. waves
sve Hgsly co 30 vovcived which diter in cernieeLoqeaey By <ove-a
Srecsur mares, Uowkesprt civil tsetse Ie gh

Sf as cule mp oe ely intact eaqatesses sol plow elas
between analogs componente of the ewe Wavén sed nee co
siderele Tr the inportant ti which ie ranrire are lentil

Inequerey tHe ie rm lenger trie on phooe and ite dependence on
preter and tzeasmissiom phenomena must be taken inca eowuunt
{This enee wil be ncorse fur Fat shay, the present work being

Finiced to a wonsideration of tle phenuens mere ni she
Adesection of distinct frecuencier

The sist inontant.nlesied faeyueacy whic is guseent in
the ougpus of Lae detectors ihe eas woke letween The love esi
Iie sometimes earelessiy asumsed that ifthe Fecuency of this beat
note is duced below the-aulinlerange the only reusing iterfvenre
wil be de uch sec Grom the wes stan, Sach st he
five and it sll be shown Inter on thot when the best frequency
Felacel Llane the lie rage tr lo era, thee remains a eon

tf spuriony Frege which wl it odice a interfering legend,

‘When the undesired carcer ie of relatively smal ntancty this back

round ie a great des! suonger than the interfering speech. Tt is

Shereore desirable to obten quantitative data om the iatetering spec
Pee, LE, Jan, 93
2 SRLL SYSTEM ToeustcaL sovRNAt

‘rum which accu in the regciver tai, trams of the intensities
ni degrees of modulation ofthe a signal

Tis to be eapected that the reults obtained wll depend to some
stent ae leat, on the typeof leertoe whichis used. The square law
‘Character sfc appeosimation that of say detecting device
{Which i worked vero sc mall sange and hence an als of thi
Characteristic may he expected to serve as an exelent guide to general
Seector yertormaree. Wea Large signals are impresed onthe
Aletector the functioning of the device may aporaximate more closes
Corhet ofthe eel stvght Te eeeeeor, It hs fen el thats stad
of chee twn tyes woul Gurtish data from which the pesformance af
any incermediae yet descetor could be infeed without greac error
Ae fhe poles ofthe guar la lle fs very much the simpler it
sel he cited fast

Marrrnaricst, Axaasts

“These will be assumed te brosdeasting aacions transmitting nt
foeslenciee whieh differ ly a relaive'y small amount, the brat fee
ssueney Being restrict ce the audible range or less Tach of the
CGoricte wil be aetrmer 4 he stodulaced Uy a single aio Feeney,
the medulading frequencies ai the 90 statione Teng, in gener,
Alife. The tote, signal imprensol on the ceceving detector wll
‘he Le of the form

ABLE eon ihe ane Fal fom coe oot,
a whic

‘i che total alternating valage impress on the deacta:
is the ample of the dsied corer.

‘is the comin of Tne uadesived carrier.

‘isthe cngree nf enedulation of the desired sigoal

sp io the degre of slat of the weird clgpal
s.fby isthe Sresucney ol the desired carve.

“o/2 the Ceeueney of the ymeesved carver

{its i the ficnteacy of the desired mexiulation

ile the Fequaney othe undesired modulation

Savane Law Drescro

‘We shall rt euppoe thie signal toe impressed on a detector whic
will be assumed t have g ehiriclernic in the neighborhood of the
pesating eine, of the form

bode Aes c)
An exresion ofthis type wil accurately vemosen:« soll portion of
ny continuous charatesstie, The pre-ent analysis requizes thet the
Impressed es {shall eof small amps nv order that the its af
the portion of the characteristic thas represen! rn wo be econ
‘This weston i necteary in treating square law detectors

"The inaie feequeney ota of the eetectoe will be due entirely to
Ie secon der term in (2). Heer it will be sufeent, for our
pean, to audeae the expression for =. We are interested primarily
in the ration of the amplitudes uf Ue warious undesiced audio fre-
fnecocee proce the amplicude ofthe esi! sign’ of Fequoney
fi2e. buch ¢ ratio wil be fesignate a a telative amplitude, Neg
Tesdg Greuit constants, eres vaieh wil apply equaly in ‘all the
shimendons faethe variose frequencies. the amplitae of the desire
fomponent of the aia frequmney ula is ready show to be F
‘The expression low is ace to Sept power sins wl tse aap
tude of ea frequency nanverted toa Felative ampli by: diving
by EY? The cove in hal yields twelve undesired audio frequencies,
Le selative armplitides of whic ane Hsted table [Before en
tieating on theve results we wall sider che staiabt line detector

|e
|
% a | paean LJ

in whieh 2 =

“Tur Sraanssr Lise Dusucron

In moking aneiyacs of rectiestion by a straight line deteesor i is
‘custom to tedue te st 1 the vious impeessed ado frequencies
tov single radi frequency, the sepitade and phase atleof wich are
ow functions of tise. The most common eximple af ths type of
Srestment iss combinasion of the earse al two aide bands of ingle
eauenry atulation into the fuss expression for a modulated
4 BEL SYSERM 2RCHSICAL JERS

wave in which the amplitude of she radio frequency is an adn
Frequency fonction, Tn thie ose Une alin Fequeney pleaw nne
samstants Th Ube cae of single Crequeiy seul tot wits ome
‘band eliminaced there are impressed on the detector input only two
frequencies. These may be combined in a well known manner.
‘Thus it the impressed voltages are of the form acaas and boos, thea
the amplitude is given by

ETB 208 208 (3h @
‘The expression forthe phase angle will not be given here aa it can be
iowa Unt if and 5 ace unequal apd che diference between the
fejuencies 4:25 and ye is amall compared with either frequency,
then the vasiation af the phase ansle with time may be neg ected i”
comping the aio Frequeney oomponents. Ts the pretnt cae we
fave two radio fequeney waves the amples of which ase wol
fumstats but are slow fates ine aon hese may be ebecated
fora and bin (3), Thus the effective amplitude of the total input
Signal may be taken tobe

SNA + B+ AB cos, a

in whieh
A= FAW Meee 8,
Balt moat,

and
“The problem then coves itaelf into an analyie ofthe detection, bya
stright line detacto, of & single radio frequency component. The
resuls of auch a analysi are well known and it ean be readily shove
that the audio fequency output may be obtained, excep fora factor
of proportionality, by eselving the amplitude int ies audio frequeney
compocenss, In the present ease the amplitude eo be resolved is
iver by (4) which may be writen

Sa VOSS ame,
‘The itesering signal will lee tee away eee Ha the ie
fre signal rd hence A? Bt > 24, Trem whic it ftw thal
[A= BY > 2ABU1 — orm at) Heave the sical may be expanded
Thy the binomial heowean, giving,

ABUL = cos wf)
Snapp able

ANB — oo wl? A8B NL ~ 8 HE eg
2b vaaBy 8
Ic isto be observed thar each of the tems of this ceies, exept the

Fst eantaiss time in tre denominator and henre fst expen

sve naressars. The eenominatoce of the vatiou® tm

pane bythe Tinonvad there iv sues way as rs pall the
fig Ui in eters, Ue expansions being i

Tre

powers at
EE cos pF Lae cos

Fy the proper erigonametri rev sfrmaion i scm co reduce the
inl express fur Sn Freqormes Fy 4. ae the sts and ele
ness of the vativus multiples of these guentities An agditioaal
Miser of this analysis pfoen ta aypendis, Im order thatthe
vtioue series involved may coawverge with a manageatle degree. of

pity i fsneceseory lnil the ehative annitencl Taetetertering
fatriees aad the degrees of soodulation ae wll. Consequently the
Solutions are sesticted vo intensiis of the teeing cari 0.
so the dese carves and to depres of medulatin of cher nigasl
ging form C195. Tho leis mae aly ease we are
terete che fntesteree i a reaFvey weak gral, the inter
ferme eauved by a signal, tae carier amplitude of which is eceater
Than. of thst ofthe desire carrer welt Ling near the ealerale
Time inthe majviey of eaees. Tae upper value for che mndution of
3 is anpioxinvtely eyjal to Uke avecage dag ob duit
lation employing ce deep modulation as i practical, only the peaks
runsing up 1 neasy usiey. ‘The value of 0.1 Zor the Tew Limit is of
ours tranaqested by soft pastaze in spect or music. Llomeve:, the
‘age here speciied be aullicienty lage gove ma esclleut idea ut
‘whet may be espacsed vom various degree 0: riodelation of esi
rd incorfering signals andthe eesulcs ot more estiere eats anay be
inferred trom the data he-e developed. Under these its i feane
hat the anly audio Iesqueases of any inpowcanoe wilt pear ie
the outpus ae
Cowranrsons Betas: Diemrorons

11% wow possible la ake w oompavicnn between the performance
of the wirnight line and the rqiare sw sleieesor a Pas. cod are
Stow. the wate aamplicides oF de ulefering Lenses in the 0
tases for vans degiees of maton. ae data fo the rjuare kt
fase ane vlna By dashed es avd for che staighs Hine case by
fold lives an wlexe che ewe evince de woted nt the hgwees. Le
|e to be otel dal Lie csqesson foe the amplitude of che sil
rogue Q2x is a complieaer! ction. However, computation
thom that oer lsc rage in-wFich we see interest, the value of tis
fxpression sees aol iter From 25% by more thon por cent aly
Uerfiny, 11s vale has bern sswumed ia competiog the relative
ampBnces of the other Scequerei

Peli Jie ne. selng ealaee se nete in eam the te.
roses in sing ofthe rest.” This's partiulary eviceread by
Tie carr lea te of fegueney wee apaliede of which die:

iw Ie bow casts hy av miapymecable ameure, The sturines fe
tints fe a2e abe sae qeacticallyideoteal for both elector
lwo ine, however, sew ivipetant isrences a fli
‘The gloup af sprsins frequencies ot gular vekcity @ +g bs,

which is of apprevailefnpaviesse in esque Tw aa, i emily
faut trom the romp wiagkicace considered whch a straight Hoe
Aetector employe. The frequencies (p La})2e se gieace inthe
Equare Law tate ener the range wach ae have coilere, bet the
Cave which reprrsents thea hae aezaller slope ham in the straight
ine rane al for Tasge values che ilenering sign “he intensities of
hee eequcnies woud be clatrely les withthe aye hw deter.
‘The ntety of the undeszed spech qi deistly Tes fa she straight
ing case than fa the aque lam re ha Ube cope of the g curves
about the same fo bora exert for AF = us — 0.8, Te vol inevest co
nese thas the ine fering speech eve on che era ine dececoe
every match less in fuensity than would be tae case if the sting
(Cearesiual wece aba, ant teas the wiriaoa of the ample of
Tlie feneace with Intensity’ 98 the undesnsl cuice is greater when
tine derived trsqueney is preset. We have here an analytical desesip=
ion th aniline gen ler which occurs whew arin wamodu
Teel varies issoverved siillancousy with + weale modulate sig:
or exmirle, when (B= 01 ic ean moron from Hig 1 thas he
relative alte of toe sneponent of Freyrrsiry y2y is QOO6S fu
the ease of the stig line deletes. Uf thie component were a
Affi Ly the present af the trong! St would have an sampled
proportions! eo cm aoa elatve avoptivade 0 oa AF which for the
Vries ise considered & 4. Llenee the “aarkina" effet i here
Frstueeile fora lucia of dh

Tent muy Le meptionel as sie ate i the eww of ube suse
ling deter sertsin troquencies a msl azaplitude which are emticely
LIbeent frort ie sqeace law rove, -Honever, rn Frequency is show
the relative amp site of whic sf than 0.01 forall Fons pals of
iluesaf i cnn gesurhtsoqueniesaneaninpartacs. An exteption
Fe aide with regard eo 9 she alway Less thar 01 ves the
range considereé but sft fog ehe sake of womgarisan with the
saqnire ba reat

yenn Coxsinesos oF Disuceae Outer

Tre eecrxl armntie tthe ceive signal
Ine eguare law tive, Ik of thr nature of d'stortion which ie inde
Dena of the inisfeeace and ray be amited rom she eansideation
De nadesired ain feyuencis whies re ees of the interference,
Frou Figg, {tod fe fg evidert that the mose ieporkr itevfering
frequencies are thew of aagular veily. ge p se wand Dg
2. the few Dein of mpersiroe way ia che ease of the equate law
ieceton, Tl ix nth these Srequencic together wich that of Tie
iiersngspeesig/2> ha. we shal be chiefly eoerned,

When the relative margins of t3¢ interfering trequenses, whieh
are taulased or page fare snaliped hy BAM, che xe tne qwauiies
fa proportional fe fe alwoluce magus of ese Eres. LL
fet le noted shat the frecuonciee of greatest interest have absolute
‘agate: ie” are liar Canetions of 2 or 3 except {°
Soh peoportnal nana v4 whic’ ie independensof bol 3E
Si ana vl, Testoce, be nvaleced by che sy of modulation
inploped st either stacks Incase there are seca Frequencies

of impastance only
tse. i the avdulatinn ese statins fhe eatin eequenty waves
Tel be of the form BVT 41%, cos pt + Sie eas Bet ~~") com wt a
BU oor gt meen gl fo} com Meeevery Frequency of
the farmer ene which vane ge afar fie amp me shall
sow have several frequeies respectively proportonal co,

‘ile an avalogome new fron wll orrsnone: tthe ores troguencles

Se
Eamermacvemne
anil
: WZ
— val
iE i
be = eaine
: | Le

cuntaining n. Hestse we shall have Gxo siequeney apeetee, derived
Fann he sei speueh sevirii eonsaining the p's Eu oe of the
spectra wil be shifted yparard in frequeney by az amoun® 42s and
the ether downward br the some amount. ‘Tao additonal specera
‘vibe derived in similar rarer from te sesived speech epeecrart
Containing theg’s, The feequencine nf he type (P +g =} wll be
DEFECTION OF TRO sropuLarED waves °

rmamerous a8 chete willbe a progct of the As wil eel of che as
Himeves, these sce of even tmderate feurtance aly when the
rriuation af bot stations ars high anc a square law dereczor is
‘eaployed atthe receiver.

ence we my pictire the interferenes ax mae wp wiley of &e.
pived fesqueney spect of the twpe mensioned abuve, of a co

E
E =

ti zi
1

nVAAy Ae PULL

ns eet atin

bat and ofthe interfering speech, which ix wrk bt impor Lant because
ts inteligitley. The results inthe cae f a strigl oe detector
Mrould soe be very greatly dtorent. The ferquencies of the type
[pba = wide woud Se neglisile, the two apeetea derive Fem
2 ob sewoule be mete less importa anderen new Tal rar sal
race poedctfrqenei wule aqme
0 (BELL SYSPRA™ TRORNTCAL 16)

In estimating the interference the caver heat can be considered by
feel ad tom the deta st sar ere cathe derived the arees around
teach of cn stetione having approrinntely the sane curier aquest,
Inside cf woieh the arplitinte ef -he beat note Wil be dows 2 given
thusaber of db from that of she esr specc. he same is ue of che
limosering speecs wher i i dllesent “vom the dested speech, ‘The

_ "Kosai oF cannen aun sices

frequencies (4 whites @ + ahi2e. p 4 = o)2e, ete. will combine
to forma cisturing huckgsouad which we shall desigmteas "displaced
Se band interfere,” This zaay be takes 10 inchade all f che
interfering feequeneice escept thew u! uke undesired speech and fs
tnttely nnimpaveant harmonics. (The requeney 26/2 ie net here
layed fates trequeney.)